Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
256 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20260789 | C2 | semidirect |
| 3. #20260785 | C2 | semidirect |
| 4. #20260459 | C2 | semidirect |
| 5. #20260458 | C2 | semidirect |
| 6. #20260458 | C2 | semidirect |
| 7. #323×C97 | C2 | semidirect |
| 120. C97 | #1469 | semidirect |
| 127. #323 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690796 | 2 |
| #20260789 | 2 |
| #20260785 | 2 |
| #20260459 | 2 |
| #20260458 | 2 |
| #323×C97 | 2 |
| #1469 | 97 |